The sentence itself doesn't give a clue about whose father Dima doesn't know. But the conversation in which this sentence is used will provide all context to make it clear. It could be two people talking about an orphan (and his father), or two brothers talking about a friend (and their father).
It looks like it's about Dima's father, as if they were talking about not his father, they would call this man just a man or they would definitely say whose father Dima does not know, and if there is no specification, obviously it is about his father. (Sorry if I have mistakes.)
FEI (For Everyone's Information): In short form, savoir is to know things, connaitre is to know people. See:
The words are often cut off in the slow versions. It is extremely time-consuming and difficult to edit sound down to one word, especially when a word is being extracted from a string of words (a spoken sentence). If it's too long, you often get pieces of the previous or subsequent word mixed. Getting a perfect sound for the slow track would be extremely expensive and time-consuming. I rely on the slow version to get the basic word down, but listen to the fast track for endings. Sometimes you just have to make an educated guess, usually based on the module you're studying.
This is true of every language on Duo - and in other language programs, too. Often, you get what you pay for.
In English, the presence or absence of an article or determiner turns "dad" into a proper noun - a name for a person, e.g. "Dad is a great guy". With the article, "dad" is just a descriptive noun. "My dad/father/papa." Perhaps most clearly"Dad is my dad" is like saying "Henry is my dad."
знать (znatʹ) [znatʲ] impf (perfective узна́ть) "to know" From Old East Slavic знати (znati), from Proto-Slavic *znati, from Proto-Balto-Slavic *źnōˀtei, from Proto-Indo-European *ǵnéh₃t, from *ǵneh₃- (“to know”), whence English know, cunning, canny, notice and gnostic (the latter two via Latin and Greek, respectively), Latin cognoscō ("I know", whence Spanish conocer, French connaître, Italian conoscere, Portuguese conhecer), Ancient Greek γνωρίζω (gnōrízō, “I know”) and γνῶσις (gnôsis, “knowledge”), Albanian njoh (“I know, recognise”), and Persian شناختن (šenāxtæn, “to know”).